Efficient Algorithms for Computing Nœther Normalization

  • Amir Hashemi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)


In this paper, we provide first a new algorithm for testing whether a monomial ideal is in Nœther position or not, without using its dimension, within a complexity which is quadratic in input size. Using this algorithm, we provide also a new algorithm to put an ideal in this position within an incremental (one variable after the other) random linear change of the last variables without using its dimension. We describe a modular (probabilistic) version of these algorithms for any ideal using the modular method used in [2] with some modifications. These algorithms have been implemented in the distributed library noether.lib [17] of Singular, and we evaluate their performance via some examples.


Polynomial Ring Computer Algebra System Hilbert Series Input Size Hilbert Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Amir Hashemi
    • 1
    • 2
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.Inria-Salsa project/ Lip6-Spiral teamParisFrance

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